We derive closed-form expressions to price European calls and puts assuming the cash flows of the underlying asset or project are normally distributed. This approach has important advantages in the context of real options applied to infrastructure projects when compared to the Black-Scholes...

We show that the model for fractional cointegration proposed by Granger (1986) allows for a representation of the solution that demonstrates the fractional and co-fractional properties. Moreover, we show that the stability of the system can be studied by means of the argument principle inherited...

We study modification properties of stochastic processes under different probability measures in an initially enlarged filtration setup. For this purpose, we consider several pure-jump Lévy processes under two equivalent probability measures and derive the associated martingale compensators...

In this article we provide a new definition of concave conditional performance measures. We prove a duality to conditional risk measures. New dynamic performance measures based on dynamic risk measures are established. We are able to derive dynamic bid and ask prices with respect to a stochastic...

In this paper, we introduce an extension to the LIBOR Market model that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LIBOR...

The purpose of this paper is to develop certain relatively recent mathematical discoveries known generally as stochastic calculus, or more specifically as Ito's Calculus and to also illustrate their application in the pricing of options. The mathematical methods of stochastic calculus are...

Classical quantitative finance models such as the Geometric Brownian Motion or its later extensions such as local or stochastic volatility models do not make sense when seen from a physics-based perspective, as they are all equivalent to a negative mass oscillator with a noise. This paper...

We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local...

We introduce a class of analytically tractable jump processes with contagion effects by generalising the classical Hawkes process. This model framework combines the characteristics of three popular point processes in the literature: (1) Cox process with CIR intensity; (2) Cox process with...

The design of environmental trading systems induces specific features of the emission permit price dynamics. In this paper, we evaluate the performance of reduced-form models for emission markets that capture these features in a simplified way and are still feasible for calibration to permit...